Possibly a stupid question, but are you using the wireless dongle that came with the headphones? I have the same headphones and run arch as well, and my pc recognizes the dongle as “Audeze Maxwell usb” or something like that.
I’m running pipewire for my audio system and iirc it worked out of the gate with these headphones, though I did some modifications to get digital surround sound working too.
Oh sorry I was in a rush reading your post the first time and fully missed that your wireless adapter was broken lol. Do you have a 3.5mm audio cable to use? I honestly don’t even know if the USB port supports audio but my gut feeling would be charging only (can’t imagine why they’d bother putting a DAC in the headphones). I won’t have my headphones or my pc for a couple days but I can poke around with this after that if you want anything tested on another similar setup, by then.